## My Teaching Philosophy:

My courses are based around encouraging students to actively think about how to arrive at a solution, while I guide them through the process of mathematical and logical reasoning. My objective is to demonstrate a central truth about mathematical thinking: the most productive way to approach a challenge is by thinking about what procedures are appropriate for a particular problem and in a particular context, not by simply knowing how to perform different procedures. I treat mathematics as a puzzle to be explored and played with. From the first day of the semester, I continually communicate to my students that there is no such thing as a “math person;” instead, mathematics is based around logic and reason, and logic and reason are central to what make us human. My hope is that in this way I can break down the math anxiety some students may have by transforming mathematics into an engrossing exploratory process.

For a detailed description of my teaching philosophy, please see my teaching statement.

## Courses Taught at Penn State:

- MATH 111:
*Techniques of Calculus II*. (Spring 2020)- Multivariable functions; partial differentiation; multiple integrals; first-order linear and separable differential equations; applications.

- MATH 220:
*Matrices*. (Fall 2019)- Matrix algebra; linear transformations; subspaces; orthogonality; diagonalizability; characteristic polynomials; applications.

- MATH 231:
*Calculus of Several Variables*. (Spring 2019, Summer 2018*)- Three-dimensional analytic geometry; calculus of parametric curves; partial differentiation; applications.

- MATH 230:
*Calculus and Vector Analysis*. (Summer 2019*, 2018*; Spring 2018; Fall 2018, 2017)- Calculus of parametric curves, multivariable functions, and vector fields; multiple integrals; line and surface integrals; Green’s theorem, Stokes’ theorem, and the divergence theorem; applications.

- MATH 251:
*Ordinary and Partial Differential Equations.*(Spring 2017, Fall 2016)- First- and second-order equations; higher-order linear equations; Laplace transforms; systems of equations; Fourier series; partial differential equations.

- MATH 110:
*Techniques of Calculus I.*(Summer 2016)- Functions and graphs; techniques of differentiation and integration; improper integrals; applications.

- MATH 021:
*College Algebra I.*(Spring 2016)- Linear equations and inequalities; quadratic expressions; algebraic fractions; negative and rational exponents; radicals.

*These courses were taught online through Penn State World Campus.

## Other educational experience:

**Penn State University Department of Mathematics**,*MATH 141 Digital Teaching Assistant*(Summer 2017)- Facilitated online discussion board and recitation sessions for online course in Calculus II.

**Penn State University Department of Mathematics**,*MATH 022 Digital Teaching Assistant*(Fall 2015)- Led online recitation sessions and graded assignments for online course in College Algebra II.

**Hamilton College Department of Mathematics**,*MATH 337 Grader*(Spring 2015)- Graded problem sets for upper-level undergraduate course in Partial Differential Equations.

**Hamilton College Quantitative and Symbolic Reasoning Center**,*Peer Tutor*(Fall 2012 – Spring 2015)- Tutored eight to twelve drop-in students a week in calculus, linear algebra, differential equations, general and organic chemistry, and biology.

## Private tutoring:

In addition to teaching, I also privately tutor. While privately tutoring, I focus on developing a student’s independence in mathematical thinking. Just as when I teach classes, I believe critical thinking should take precedence over knowing facts. If you are interested in private tutoring, you can email me at dkv5049@psu.edu.